Operations with Scientific Notation

Operations with Scientific Notation

A compact way to write Very LARGE & Very SMALL numbers​

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

Standard ---> Scientific Notation

Scientific Notation

​

Multiple Choice

Scientific Notation is used to represent __________.

• Very Large Numbers

• Very Small Numbers

• Very Large & Very Small Numbers

• Height

Multiple Choice

Which of the following is correctly written in Scientific Notation?

• $$65\times10^2$$  

• $$4.5\times10^{-7}$$  

• $$11\times10^2$$  

• $$0.98\times10^{-3}$$  

Multiple Choice

To be in Scientific Notation, you must write all exponents with a base of ___?

• 1

• 5

• 10

• 100

Multiple Choice

The first number in Scientific Notation can be less than 1.

• True

• False

Multiple Choice

Write this number in Scientific Notation:

65,000,000

• $$6.5\times10^6$$  

• $$6.5\times10^{-6}$$  

• $$6.5\times10^7$$  

• $$6.5\times10^{-7}$$  

Multiple Choice

Write this number in Scientific Notation:

0.00000784

• $$7.84\times10^{-6}$$  

• $$78.4\times10^{-6}$$  

• $$7.84\times10^7$$  

• $$7.84\times10^{-7}$$  

Get out a piece of paper and get ready to write some info & an example!

Step 1: Make sure exponents are the same. ​

**Use "LARS" to move the decimal if needed**

Left Add​

Right Subtract​

​

​

Step 2: ​Add or Subtract the numbers. Keep common exponent.

​

ADDING & SUBTRACTING

Numbers in Scientific Notation​

Step 1: Make sure exponents are the same. ​

**Use "LARS" to move the decimal if needed**

Left Add​

Right Subtract​​

​

Step 2: ​Add/Subtract the numbers. Keep common exponent.

​

​

Add

or Subtract

​EXAMPLE

Step 1: Make sure exponents are the same. ​

**Use "LARS" to move the decimal if needed**

Left Add​

Right Subtract​​

​

Step 2: ​Add/Subtract the numbers. Keep common exponent.

​

​

Add

or Subtract

​EXAMPLE

Step 1: Make sure exponents are the same. ​

**Use "LARS" to move the decimal if needed**

Left Add​

Right Subtract​​

​

Step 2: ​Add/Subtract the numbers. Keep common exponent.

​

​

Add

or Subtract

​EXAMPLE

Step 1: Make sure exponents are the same. ​

**Use "LARS" to move the decimal if needed**

Left Add​

Right Subtract​​

​

Step 2: ​Add/Subtract the numbers. Keep common exponent.

​

​

Add

or Subtract

​EXAMPLE

Multiple Choice

Add/Subtract & write answer in Scientific Notation:

$$(3.4\times10^3)+(1.1\times10^3)$$  

• $$4.5\times10^3$$  

• $$45\times10^2$$  

• $$2.3\times10^3$$  

• $$4.5\times10^6$$  

Multiple Choice

Add/Subtract & write answer in Scientific Notation:

$$(1.8\times10^{−1})+(7.3\times10^{−3})$$  

• $$1.873\times10^{-1}$$  

• $$1.873\times10^{-3}$$  

• $$1.873\times10^{-2}$$  

• $$18.73\times10^{-1}$$  

Multiple Choice

Add/Subtract & write answer in Scientific Notation:

$$(8.17\times10^4)−(2.6\times10^4)$$  

• $$5.57\times10^4$$  

• $$557\times10^{-3}$$  

• $$5.57\times10^{-8}$$  

Multiple Choice

Add/Subtract & write answer in Scientific Notation:

$$(9.5\times10^{-5})−(3.4\times10^{-5})$$  

• $$6.1\times10^{-10}$$  

• $$6.1\times10^{-5}$$  

• $$6.1\times10$$  

Get out a piece of paper and get ready to write some info & an example!

Step 1: Multiply/Divide the numbers.

​

Step 2: ​Use Product Rule or Quotient Rule for Exponents!

​

Step 3: ​Make sure final answer is in Scientific Notation.

Use "LARS" **Left Add, Right Subtract**​

​

​

​

MULTIPLY & DIVIDE

Numbers in Scientific Notation​

Step 1: Multiply/Divide the numbers.

​

Step 2: ​Use Product Rule or Quotient Rule for Exponents!

​

Step 3: ​Make sure final answer is in Scientific Notation.

Use "LARS" **Left Add, Right Subtract**​

​

​

Multiply

or

Divide​

​EXAMPLE

Step 1: Multiply/Divide the numbers.

​

Step 2: ​Use Product Rule or Quotient Rule for Exponents!

​

Step 3: ​Make sure final answer is in Scientific Notation.

Use "LARS" **Left Add, Right Subtract**​

​

​

Multiply

or

Divide​

​EXAMPLE

Step 1: Multiply/Divide the numbers.

​

Step 2: ​Use Product Rule or Quotient Rule for Exponents!

​

Step 3: ​Make sure final answer is in Scientific Notation.

Use "LARS" **Left Add, Right Subtract**​

​

​

Multiply

or

Divide​

​EXAMPLE

Step 1: Multiply/Divide the numbers.

​

Step 2: ​Use Product Rule or Quotient Rule for Exponents!

​

Step 3: ​Make sure final answer is in Scientific Notation.

Use "LARS" **Left Add, Right Subtract**​

​

​

Multiply

or

Divide​

​EXAMPLE

Multiple Choice

Multiply/Divide & write answer in Scientific Notation:

$$(1.3\times10^9)\times(4.5\times10^9)$$  

• $$5.85\times10^{18}$$  

• $$5.85\times10^9$$  

• $$5.85\times10^{-18}$$  

• $$5.85\times10^{-9}$$  

Multiple Choice

Multiply/Divide & write answer in Scientific Notation:

$$(9.8\times10^{−24})\times(7.5\times10^{27})$$  

• $$73.5\times10^3$$  

• $$73.5\times10^{50}$$  

• $$7.35\times10^4$$  

• $$7.35\times10^2$$  

Multiple Choice

Multiply/Divide & write answer in Scientific Notation:

$$(6\times10^{-6})\div(2.83\times10^1)$$  

• $$2.12\times10^{-5}$$  

• $$2.12\times10^{-4}$$  

• $$2.12\times10^5$$  

• $$2.12\times10^{-7}$$  

Multiple Choice

Multiply/Divide & write answer in Scientific Notation:

$$(2\times10^5)\div(2.7\times10^{-4})$$  

• $$7.407\times10^{-5}$$  

• $$7.407\times10^6$$  

• $$7.407\times10^8$$  

• $$7.407\times10^9$$  

If you move the decimal to the left, add one to the exponent on 10 for each move.

​

If you move the decimal to the right, subtract one from the exponent on 10 for each move​.

Moving the Decimal:

To be in Scientific Notation, the first # should be between 1 and 10, multiplied by a power of 10.

Remember:

REVIEW:

Operations with Scientific Notation